The state House of Representatives heard 56 hours of public testimony over five days last week. On Friday night, the House passed the marriage bill by a 30-19 vote.
The state Senate, which passed its version of the same-sex marriage bill by a 20-4 margin earlier this year, passed the House version when it met Tuesday. Abercrombie has said he will sign the bill.
The compromise bill allows same-sex couples to get marriage licenses as early as Dec. 2.
Republican state Rep. Bob McDermott said in a letter to Abercrombie on Friday he will file a request for a temporary restraining order if the bill passes, the Honolulu Star Advertiser reported Tuesday. A state judge has said he will hear the case if the bill passes.
Hawaii will give same-sex marriage proponents its second big win in two weeks. Illinois lawmakers passed a same-sex marriage bill on Nov. 5, and Gov. Pat Quinn (D) said in a statement he would sign it at a public ceremony on Nov. 20.